Basically, they work just like pirate bases, but slightly altered in one way or the other.
Sleeper cells are idle. As far as I remember, they can cause stability drop in a select colony on occasion, but nothing you can do about it.
Both disturbed or active cells you can fight (unlike pirates, that you can only fight once they're active) on their home turf, which obviously means station busting. An active cell, if left unchecked, can quickly cut into your stability and profit margins. Same way as with pirates, asking around the bar on one of your colonies guarantees to give you the info on the system the enemy is located in (unlike pirates, it costs you some pocker change now). Disruption lasts a year by default, but it may also cause the cell to go "sleeper" mode, which, IIRC, randomizes the timer in either direction.
As with pirates, having your colonies in one system drastically reduces the amount of babysitting you'll have to do yearly. However, having 11 planets in a single system myself, I have to do the disruption on two yearly timers, and not one - I'm not sure if it's intentional or not.